Using electromagnetic waves to remove near wellbore damages in a hydrocarbon reservoir

ABSTRACT

Methods and systems for removing near wellbore damage in a hydrocarbon reservoir are described. In one example implementation, an antenna is positioned inside a wellbore in a location corresponding to a formation where near wellbore damage occurs. The wellbore extends from a surface of a hydrocarbon reservoir downward into the subterranean structure of the hydrocarbon reservoir. An electromagnetic (EM) wave is transmitted to the antenna. A portion of the EM wave is irradiated at the formation. The portion of the EM wave removes the near wellbore damage at the formation.

TECHNICAL FIELD

This disclosure relates to removing near wellbore damages in ahydrocarbon reservoir, for example, using electromagnetic waves.

BACKGROUND

In some cases, productions of a hydrocarbon reservoir can be impacted bynear wellbore damage. In the context of the oil and gas industry, anear-wellbore region refers to rock formations in the subterraneanstructure that are in the vicinity of the wellbore (for example, about afew centimeters from the rock surface of the bore-hole wall).Near-wellbore damage refers to flow restrictions caused by the reductionof permeability in the near-wellbore region during drilling, completion,or workover operations. Near-wellbore damage can significantly affectproductivity of the well.

In wellbore drilling operations, a drilling fluid is flowed from asurface through a drill string and into a drill bit drilling the rockformation. The drilling fluid flows through the drill bit and returns tothe surface through an annulus formed between the borehole wall and thedrill string. The drilling fluid is also referred to as the drilling mudor the mud.

SUMMARY

The present disclosure describes methods and systems for removing nearwellbore damage in a hydrocarbon reservoir. One method includespositioning an antenna inside a wellbore in a location corresponding toa formation where near wellbore damage occurs, wherein the wellboreextends from a surface of a hydrocarbon reservoir downward into thehydrocarbon reservoir; transmitting an electromagnetic (EM) wave to theantenna; and irradiating, from the antenna, at least a portion of the EMwave at the formation, wherein the portion of the EM wave removes thenear wellbore damage at the formation.

Other implementations of this aspect include corresponding systems andapparatuses.

The details of one or more implementations of the subject matter of thisdisclosure are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram that illustrates an example well system,according to an implementation.

FIG. 2 is a schematic diagram that illustrates an example treatmentzone, according to an implementation.

FIG. 3 illustrates an example method for removing near wellbore damageaccording to an implementation.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This disclosure generally describes methods and systems for removingnear wellbore damage in a hydrocarbon reservoir. The near-wellboredamage can occur in many situations. In one example, the near-wellboredamage can be caused by incomplete removal of filter cake formed fromdrilling muds. During drilling operations, filter cake is formed on thesurface of the wellbore to reduce the fluid loss. The filter cake isremoved after the drilling operation and before the cementing operation.Sometimes, fluid or surfactant solution may be needed to remove thefilter cake. If there is a permeable region near wellbore, the fluid mayflow to that region, and some portions of the filter cake may stay inthat region. Due to ineffective removal of the filter cake, theeffectiveness of the cementing operation of the well may also beimpacted. An ineffective seal between rock formation and the cement mayresult in gas or fluid migration.

In another example, the near-wellbore damage can be caused by skindamage or near wellbore plugging from stimulation fluid in open-holehorizontal completions. In some operations, fracturing operations areperformed in a horizontal open hole and uncemented liner completions.Filter cake may form during the fluid leakoff to the formation. Incertain cases, the polymer concentration of the filter cake will reachto 300-400 pounds per a thousand gallons of fluids (pptg). These filtercakes may be difficult to remove.

In some implementations, electromagnetic (EM) waves can be used tofacilitate the removal of near wellbore damage. For example, EM wavescan be directed to the area of near-wellbore damaged zones and removethe near wellbore damage by irradiating on the formation in that area.

In one example, EM waves can be used to remove filter cakes by degradingthe polymeric components in the filter cakes due to the heats generatedby the EM waves. In one scenario, oil based muds with water internalphase can be heated to create pressure inside the filter cake. As aresult, filter cake may fall in the wellbore and may be removed from thewellbore. Water-based filter cakes can be heated and the pressurecreated by sudden water expansion can facilitate the detachment offilter cake from formation. This technique may mitigate near wellboredamage caused by incomplete filter cake removal.

In another example, EM waves can also be used to remove the skin damagecaused by fluid in a near wellbore region. In addition, EM waves canremove and damage caused by fines migration by creating new fracturesand thus increasing permeability in the near wellbore region.

The EM waves can also help break the emulsion by locally heating thewater molecule in the near wellbore region. In some cases, EM waves canhelp break the surfactant molecules that are stabilizing the emulsion.EM waves can also break natural surfactants from produced oil thatstabilize the emulsion. EM waves can be used to accelerate or triggerthe degradation of the polymeric based diversion materials removal.

In some implementations, EM waves can be used to fracture the rockformations in a subterranean structure. To fracture rock formations, EMwaves having low frequencies are used to provide deep penetrations intothe rock formation towards a wide area. Examples of EM waves used tofracture rocks include radio waves that have a frequency between 500kilohertz (KHz) to 5 megahertz (MHz). In addition, EM waves used tofracture the rock formations have high power, for example, in the orderof millions of watts. On the other hand, EM waves used to remove nearwellbore damage are directed to a target damaged zone in a near wellboreregion. Thus, the EM waves used to remove wellbore damage have a higherfrequency than the EM waves used to fracture the rocks. Examples of EMwaves used to remove near wellbore damages include microwaves that havea frequency between 300 megahertz (MHz) to 300 gigahertz (GHz). Inaddition, the EM waves used to remove near wellbore damages have a lowerpower than the EM waves used to fracture the rock. For example, thepower of EM waves used to remove near wellbore damage can be in theorder of thousands of watts.

FIG. 1 is a schematic diagram that illustrate example well system 100,according to an implementation. The example well system 100 transmits EMwaves to remove near wellbore damage.

The example well system 100 includes a wellbore 114 that extends belowthe terranean surface 110, and into reservoir formation 120. Thereservoir formation 120 can span a single formation, portions of aformation, or multiple formations.

The well system 100 includes an EM wave transmitter 112. The EM wavetransmitter 112 can be implemented as one or more hardware circuitelements, software, or a combination thereof that can be configured togenerate an EM wave. In some implementations, an EM wave transmitter,for example, the EM wave transmitter 112, can include a power supply, anoscillator, a modulator, a power amplifier, or any combinations thereof,that can be configured to generate EM waves to irradiate the rockformation. In some implementations, the transmitter can include asynthesized radio frequency (RF) signal generator, a free running RFsignal generator, or a combination thereof

The well system 100 also includes an antenna 115 that irradiates EMwaves. The frequency of the EM waves can be determined based on theelectric property and thickness of the damaged zone. The antenna 115 ispositioned in the wellbore 114 and close to the location where nearwellbore damage occurs. In the illustrated example, the treatment zone117 represents the area where the near wellbore damage occurs. The nearwell bore damaged zone can be located using production logs. The antenna115 is configured to irradiate EM waves 119 directly at the treatmentzone 117, to remove the near wellbore damage. In some cases, the antenna115, and the frequency and duration of the EM wave 119, can bedetermined based on the size of the treatment zone 117. FIG. 2 andassociated descriptions provide additional details of theseimplementations.

The well system 100 also includes a transmission line 118 that iscoupled with the EM wave transmitter 112 and the antenna 115. Thetransmission line can be configured to direct the EM wave generated bythe EM wave transmitter 112 to the antenna 115. The transmission line118 can be implemented using a coaxial cable, a twisted pair wire, or awaveguide. In some implementations, a waveguide can be implemented usinghollow conductive metal pipes to direct the EM waves.

The well system 100 also includes a pump 130 that is connected with apipe 132. Prior to the EM wave irradiation, the pump 130 pumps treatmentfluid into the wellbore 114 using the pipe 132. The treatment fluidflows to the treatment zone 117. The treatment fluid includes mixture ofparticles that are used to change the dielectric property of thetreatment zone 117, and thus control the penetration depth of the EMwave 119. FIG. 2 and associated descriptions provide additional detailsof these implementations. In some cases, the pump 130 can be the mudpump that is used to pump drilling fluid in the well system 100, and thepipe 132 can be the pipe that transports drilling fluid in the wellsystem 100.

In operation, the EM wave transmitter 112 generates EM waves. The EMwaves can travel through the transmission line 118 to the antenna 115.The antenna 115 irradiates EM waves to the treatment zone 117. Theirradiation raises the temperature in the treatment zone 117 and removesnear wellbore damages in the treatment zone 117.

In some cases, as illustrated in FIG. 1, the EM wave transmitter 112 canbe positioned at the surface. Alternatively or in combination, the EMwave transmitter 112 can be positioned inside the wellbore 114. Forexample, the EM wave transmitter 112 can be positioned next to theantenna 115, inside the wellbore 114. In some cases, a case can be usedto protect the EM wave transmitter 112, the transmission line 118, theantenna 115, or any combinations thereof. The case can be implementedusing a ceramic conduit. In some cases, a cable can be used to retrievethe case, the EM wave transmitter 112, the antenna 115, or anycombinations thereof, to reuse these components to remove near wellboredamage in a different area of the wellbore 114 or other wellbores.

In one experiment, a core sample of sandstone rock sample having 1.5inches in diameter and 6 inches in length was used as a sample treatmentzone. The initial permeability measured with 2% KCl was determined to be11.76 millidarcy (mD). After injection of 20 pptg guar fluid (in 2% KCl)to simulating production operations, the permeability was reduced to0.51 mD (permeability regain was 4.3%), indicating the damage occurred.In a first microwave treatment, the sample is placed in a 1000 kilowatts(kW) microwave radiation for 2 minutes. The temperature of the sample israised to 200 degrees Fahrenheit (F). The permeability was measured tobe 2.86 mD, indicating a permeability regain of 24.3%. In a secondmicrowave treatment, the sample is placed in a 1000 kilowatts (kW)microwave radiation for 3 minutes and 50 seconds. The temperature of thesample is raised to 300 degrees Fahrenheit (F). The permeability ismeasured at 6.37 mD, indicating a permeability regain of 54.1%. In athird microwave treatment, the sample was placed in a 1000 kilowatts(kW) microwave radiation for 6 minutes. The temperature of the surfaceof the sample was raised to approximately 400 to 500 degrees Fahrenheit(F). The permeability is measured at 8.50 mD, indicating a permeabilityregain of 72.2%. This experiment illustrates that near-wellbore damagecan be removed by using microwave irradiation in the order of minutes.

The size of treatment zone targeted by the EM waves can be determinedbased on the transmitting antenna, frequency of the EM waves, and theelectromagnetic property of the treatment zone. FIG. 2 is a schematicdiagram that illustrates an example treatment zone 200 targeted by theEM waves, according to an implementation. The treatment zone 200 has abase area 210 and a penetration depth 220. The base area 210 has aradius 212. The size of the base area 210 of the treatment zone 200 canbe determined based on the aperture of the antenna. The radius 212approximates the aperture of the antenna. Therefore, antennae withdifferent sizes can be selected based on the target base area of thetreatment zone 200. The penetration depth 220 depends on the frequencyof the EM wave and the electromagnetic property of the treatment zone.Equation (1) represents an example calculation of the penetration depth:

$\begin{matrix}{D = \frac{1}{\sqrt[\omega]{\frac{\mu_{0}ɛ^{\prime}}{2}\left\lbrack {\sqrt{1 + \left( \frac{{\omega\; ɛ^{''}} + \sigma}{\omega\; ɛ^{\prime}} \right)^{2}} - 1} \right\rbrack}}} & (1)\end{matrix}$

where D represents the penetration depth 220, μ₀=4π×10⁻⁷ H/m, ω is thefrequency of the EM wave, ε′, ε″, and σ represent the dielectricconstant, dielectric loss, and the conductivity of the formation in thetreatment zone, respectively. ε′, ε″, and σ can be estimated or measuredusing rock samples in the treatment zone. These parameters can also beadjusted by adding materials with known ε′, ε″, and σ into theformation.

The size of the target treatment zone can be set based on the size ofthe drilled well, data in the production logs, or a combination thereof.For example, the radius of the zone can be set to be about the same asthe drilled well. The thickness of the zone can be set to a fewcentimeters from the rock surface of the borehole wall.

For example, particles composed of elements having specific dielectricand conductivity properties can be introduced into the treatment zone.Examples of these particles include metal oxides nanoparticles or othernanoparticles that include paramagnetic components. In one exampleimplementation, these particles can be nanoparticles that are mixed intreatment fluid. The treatment fluid can be a mixture of water,proppants (for example, sand or other proppants), and chemicals. Thetreatment fluid can flow to the treatment zone prior to EM wavetreatments. The nanoparticles mix with the formation, and thereforeincrease the penetration depth. The type of nanoparticles, and theconcentration level of nanoparticles in the treatment fluid, can bedetermined based on the target penetration depth that the EM treatmentintends to reach, and the dielectric and conductivity of thenanoparticles. The concentration of the particles can be determinedbased on the average conductivity or dielectric loss of the materialsand the target electrical conductivity or the target dielectric propertyafter the treatment. For example, the treatment fluid can have a highconcentration of the particles if the average conductivity of thematerials is low and thus the difference between the averageconductivity and target conductivity is high. In another example, microparticles can be used instead of nanoparticles.

In some cases, the irradiation power of the EM waves can be controlledbased on target temperature of the treatment zone. Equation (2)represents an example calculation of w:w=σE ² +ωε″E ²  (2)

where w represents energy density converted from EM wave in the damagedzone, where E represents the strength of the electric field of the EMwave, ω is the frequency of the EM wave, ε″ and σ represent thedielectric loss and the conductivity of the formation in the treatmentzone, respectively. These parameters can also be adjusted by addingmaterials with known ε″ and a into the formation. For example, particlescomposed of elements having large conductivity, large dielectric loss,or a combination thereof can be introduced into the treatment zone.Examples of these particles include metal oxides nanoparticles or othernanoparticles that include paramagnetic components. These particles canbe introduced into the treatment zone by mixing with treatment fluid asdiscussed previously.

The irradiation power of the EM waves depends on the volume of the zoneof treatment zone, as shown in Equation (3):p=cVρΔT/t  (3)

where p represents the power of the EM waves, c is the specific heat, Vis the volume of the treatment zone, ρ is the density of the formationin the treatment zone, ΔT is the temperature change targeted fortreatment, t is treatment time. In one example, for a treatment zonehaving a volume of 0.05 m³ (area=10 m² and depth=5 mm), to raisetemperature by 200 K in an hour, the power input of the EM wave is setto 7 kW, where parameter c=10³ J/kg/K, p=2.5×10³ kg/m³, ΔT=200 K.

FIG. 3 illustrates an example method 300 for removing near wellboredamage using EM waves, according to an implementation. For clarity ofpresentation, the description that follows generally describes method300 in the context of FIGS. 1-2.

At 302, treatment fluid is flown to a formation where near wellboredamage occurs. The treatment fluid changes a dielectric property of theformation. At 304, an antenna is positioned inside a wellbore in alocation corresponding to the formation. The wellbore extends from asurface of a hydrocarbon reservoir into the hydrocarbon reservoir. At306, an electromagnetic (EM) wave is transmitted to the antenna. At 308,at least a portion of the EM wave is irradiated from the antenna to theformation. The portion of the EM wave removes the near wellbore damageat the formation.

Described implementations of the subject matter can include one or morefeatures, alone or in combination.

For example, in a first implementation, a method includes positioning anantenna inside a wellbore in a location corresponding to a formationwhere near wellbore damage occurs, wherein the wellbore extends from asurface of a hydrocarbon reservoir into the hydrocarbon reservoir;transmitting an electromagnetic (EM) wave to the antenna; andirradiating, from the antenna, at least a portion of the EM wave at theformation, wherein the portion of the EM wave removes the near wellboredamage at the formation.

The foregoing and other implementations can each, optionally, includeone or more of the following features, alone or in combination:

A first aspect, combinable with the general implementation, where thenear wellbore damage is caused at least in part by a filter cake, andwherein the portion of the EM wave removes the near wellbore damage bybreaking the filter cake.

A second aspect, combinable with any of the previous or followingaspects, where the near wellbore damage comprises skin damage, andwherein the portion of the EM wave removes the near wellbore damage byremoving the skin damage.

A third aspect, combinable with any of the previous or followingaspects, where the EM wave is a microwave.

A fourth aspect, combinable with any of the previous or followingaspects, further comprising: determining a duration of the irradiatingbased on a target temperature of the formation being irradiated.

A fifth aspect, combinable with any of the previous or followingaspects, further comprising: prior to the irradiating, flowing treatmentfluid to the formation where near wellbore damage occurs, wherein thetreatment fluid changes at least one of an electrical conductivity or adielectric property of the formation.

A sixth aspect, combinable with any of the previous aspects, furthercomprising: mixing particles with the treatment fluid, wherein theparticles are selected based on at least one of a target electricalconductivity or a target dielectric property.

A seventh aspect, combinable with any of the previous or followingaspects, where the particles are metal oxides nanoparticles.

An eighth aspect, combinable with any of the previous or followingaspects, further comprising: mixing particles with the treatment fluid,wherein the particles are selected based on a target power level of theEM wave.

A ninth aspect, combinable with any of the previous aspects, furthercomprising: determining a treatment zone of the EM wave; and selectingthe antenna based on an aperture of the antenna and a based area of thetreatment zone.

A tenth aspect, combinable with any of the previous or followingaspects, further comprising: positioning an EM wave transmitter at asurface of the hydrocarbon reservoir; and generating the EM wave usingthe EM wave transmitter.

An eleventh aspect, combinable with any of the previous aspects, furthercomprising: positioning an EM wave transmitter in the wellbore, whereinthe EM wave transmitter is enclosed in a protective case; and generatingthe EM wave using the EM wave transmitter.

In a second implementation, a method includes positioning an antennainside a wellbore in a location corresponding to a formation where nearwellbore damage occurs, wherein the wellbore extends from a surface of ahydrocarbon reservoir downward into the hydrocarbon reservoir; flowingtreatment fluid to the formation where near wellbore damage occurs,wherein the treatment fluid changes at least one of an electricalconductivity or a dielectric property of the formation; after flowingthe treatment fluid, transmitting an electromagnetic (EM) wave to theantenna; and irradiating, from the antenna, at least a portion of the EMwave at the formation, wherein the portion of the EM wave removes thenear wellbore damage at the formation.

The foregoing and other implementations can each, optionally, includeone or more of the following features, alone or in combination:

A first aspect, combinable with the general implementation, where thenear wellbore damage is caused at least in part by a filter cake, andwherein the portion of the EM wave removes the near wellbore damage bybreaking the filter cake.

A second aspect, combinable with any of the previous or followingaspects, where the near wellbore damage comprises skin damage, andwherein the portion of the EM wave removes the near wellbore damage byremoving the skin damage.

A third aspect, combinable with any of the previous or followingaspects, where the EM wave is a microwave.

A fourth aspect, combinable with any of the previous or followingaspects, further comprising: determining a duration of the irradiatingbased on a target temperature of the formation being irradiated.

A fifth aspect, combinable with any of the previous or followingaspects, further comprising: mixing particles with the treatment fluid,wherein the particles are selected based on at least one of a targetelectrical conductivity or a target dielectric property.

A sixth aspect, combinable with any of the previous or followingaspects, where the particles are metal oxides nanoparticles.

A seventh aspect, combinable with any of the previous or followingaspects, further comprising: mixing particles with the treatment fluid,wherein the particles are selected based on a target power level of theEM wave.

This description is presented to enable any person skilled in the art tomake and use the disclosed subject matter, and is provided in thecontext of one or more particular implementations. Various modificationsto the disclosed implementations will be readily apparent to thoseskilled in the art, and the general principles defined herein may beapplied to other implementations and applications without departing fromscope of the disclosure. Thus, the present disclosure is not intended tobe limited to the described and/or illustrated implementations, but isto be accorded the widest scope consistent with the principles andfeatures disclosed herein.

Accordingly, the previous description of example implementations doesnot define or constrain this disclosure. Other changes, substitutions,and alterations are also possible without departing from the spirit andscope of this disclosure.

What is claimed is:
 1. A method, comprising: positioning an antennainside a wellbore in a location corresponding to a formation comprisingnear-wellbore damage, wherein the wellbore extends from a surface of ahydrocarbon reservoir into the hydrocarbon reservoir; determining anirradiation power level of an electromagnetic (EM) wave based on atleast a volume of a treatment zone, a density of the formation in thetreatment zone, a target temperature change, and a treatment duration,wherein the irradiation power level is determined based on the followingequation:ρ=cVρΔT/t where ρ represents the irradiation power level, c representsspecific heat, V represents the volume of the treatment zone, ρrepresents the density of the formation in the treatment zone, ΔTrepresents the target temperature change, and t represents the treatmentduration; determining an energy density converted from the EM wave basedon the following equation:W=σE ² +ωε″E ² where W represents the energy density converted from theEM wave, E represents a strength of an electric field of the EM wave, ωis a frequency of the EM wave, ε″ represents a dielectric loss of theformation in the treatment zone, and σ represents a conductivity of theformation in the treatment zone; determining a penetration depth of thetreatment zone by the EM wave based on the following equation:$D = \frac{1}{\omega\sqrt{\frac{\mu_{0}ɛ^{\prime}}{2}\left\lbrack \sqrt{1 + \left( \frac{{\omega\; ɛ^{''}} + \sigma}{\omega\; ɛ^{\prime}} \right)^{2} - 1} \right\rbrack}}$where D represents the penetration depth, μ₀=4π×10⁻⁷ H/m, ε′ representsa dielectric constant of the formation in the treatment zone;transmitting the EM wave to the antenna; irradiating, from the antenna,a portion of the EM wave with the determined irradiation power level,the determined energy density, and the determined penetration depth, atthe formation; and removing the near-wellbore damage at the formationwith the portion of the EM wave.
 2. The method of claim 1, wherein thenear-wellbore damage is caused at least in part by a filter cake, andwherein the portion of the EM wave removes the near-wellbore damage bybreaking the filter cake.
 3. The method of claim 1, wherein thenear-wellbore damage comprises skin damage, and wherein the portion ofthe EM wave removes the near-wellbore damage by removing the skindamage.
 4. The method of claim 1, wherein the EM wave is a microwave. 5.The method of claim 1, further comprising: prior to the irradiating,flowing treatment fluid to the formation where near-wellbore damageoccurs, wherein the treatment fluid changes at least one of anelectrical conductivity or a dielectric property of the formation. 6.The method of claim 5, further comprising: mixing particles with thetreatment fluid, wherein the particles are selected based on at leastone of a target electrical conductivity or a target dielectric property.7. The method of claim 6, wherein the particles are metal oxidesnanoparticles.
 8. The method of claim 5, further comprising: mixingparticles with the treatment fluid, wherein the particles are selectedbased on the power level of the EM wave.
 9. The method of claim 1,further comprising: selecting the antenna based on an aperture of theantenna and a base area of the treatment zone.
 10. The method of claim1, further comprising: positioning an EM wave transmitter at a surfaceof the hydrocarbon reservoir; and generating the EM wave using the EMwave transmitter.
 11. The method of claim 1, further comprising:positioning an EM wave transmitter in the wellbore, wherein the EM wavetransmitter is enclosed in a protective case; and generating the EM waveusing the EM wave transmitter.
 12. A method, comprising: positioning anantenna inside a wellbore in a location corresponding to a formationcomprising near-wellbore damage, wherein the wellbore extends from asurface of a hydrocarbon reservoir into the hydrocarbon reservoir;flowing treatment fluid to the formation where near-wellbore damageoccurs, wherein the treatment fluid changes at least one of anelectrical conductivity or a dielectric property of the formation; afterflowing the treatment fluid, transmitting an electromagnetic (EM) waveto the antenna; determining an irradiation power level of the EM wavebased on a volume of a treatment zone, a density of the formation in thetreatment zone, a target temperature change, and a treatment duration,wherein the irradiation power level is determined based on the followingequation:ρ=cVρΔT/t where ρ represents the irradiation power level, c representsspecific heat, V represents the volume of the treatment zone, ρrepresents the density of the formation in the treatment zone, ΔTrepresents the target temperature change, and t represents the treatmentduration; determining an energy density converted from the EM wave basedon the following equation:W=σE ² +ωε″E ² where W represents the energy density converted from theEM wave, E represents a strength of an electric field of the EM wave, ωis the frequency of the EM wave, ε″ represents a dielectric loss of theformation in the treatment zone, and σ represents a conductivity of theformation in the treatment zone; determining a penetration depth of thetreatment zone by the EM wave based on the following equation:$D = \frac{1}{\omega\sqrt{\frac{\mu_{0}ɛ^{\prime}}{2}\left\lbrack \sqrt{1 + \left( \frac{{\omega\; ɛ^{''}} + \sigma}{\omega\; ɛ^{\prime}} \right)^{2} - 1} \right\rbrack}}$where D represents the penetration depth, μ₀=4π×10⁻⁷ H/m, ε′ representsa dielectric constant of the formation in the treatment zone;irradiating, from the antenna, a portion of the EM wave with thedetermined irradiation power level, the determined energy density, andthe determined penetration depth, at the formation; and removing thenear-wellbore damage at the formation with the portion of the EM wave.13. The method of claim 12, wherein the near-wellbore damage is causedat least in part by a filter cake, and wherein the portion of the EMwave removes the near-wellbore damage by breaking the filter cake. 14.The method of claim 12, wherein the near-wellbore damage comprises skindamage, and wherein the portion of the EM wave removes the near-wellboredamage by removing the skin damage.
 15. The method of claim 12, whereinthe EM wave is a microwave.
 16. The method of claim 12, furthercomprising: mixing particles with the treatment fluid, wherein theparticles are selected based on at least one of a target electricalconductivity or a target dielectric property.
 17. The method of claim16, wherein the particles are metal oxides nanoparticles.
 18. The methodof claim 12, further comprising: mixing particles with the treatmentfluid, wherein the particles are selected based on the power level ofthe EM wave.